DISCLAIMER:
I wrote this how-to from my experience installing successfully Ubuntu on my Prime.
I am in no way responsible for what you do with your Prime, even when you are following my instructions.
There is always the risk of making it worse, hardbricking your device, and this risk is completely down to you !
This is not a final version. This port is currently very unstable !
Install Ubuntu on your TF201 for testing purposes only !

3. Before trying to do anything with your device, make a full nandroid backup of the current WORKING Android system.

To do that:
- Reboot on CWM (see the sticky, at the end)
- Navigate to 'backup and restore', then 'backup'
- Wait until the full backup is done...

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- INSTALL Ubuntu -

Introduction:
To have a working Ubuntu system on the Prime, you have to:
- Extract the root file system on your MicroSD card
- Flash the bootimage right on the device

While installing Ubuntu, the only thing you modify about Android, is the bootimage. You leave the system intact,
so you'll be able to do a pseudo-dualboot between Ubuntu, and Android (we'll see that later).

Flashing the bootimage (BE CAREFUL!):
- Reboot in fastboot mode (see the sticky, at the end)
- Connect the Prime to the computer, and be sure the drivers are correctly installed
You can find the drivers here: http://forum.xda-developers.com/show....php?t=1426502
- Extract the fastboot archive 'wintools.zip' and move the file 'prime-sdlinux.blob' in the same folder
- Execute the command: fastboot -i 0x0b05 flash boot prime-sdlinux.blob
(WARNING! This command will overwrite the bootimage of your Prime! Be sure you know what you're doing!)
- Wait until the flash completes... (it generally takes a few seconds...)
- When the blue progress bar is full, on the Prime, hold the Power switch to reboot the device
- Be sure that the MicroSD card is in the Prime
- Your Prime is now booting on Ubuntu, you should see some text displaying on the screen
- Wait until the system initializes... (It takes a while for the first boot...)
You should see kernel verbose booting, displaying something saying the system is resizing a partition
on the MicroSD card...
- Your Ubuntu system is installed ! You can do the graphical basic setup, then do a hard reboot of the device !
- Good luck with your freshly installed Ubuntu on your awsome Asus Transformer Prime !

--------

- RESTORE Android -

Introduction:
After installing Ubuntu, to have Android back on the Prime, you have to:
- (OPTIONAL: Do a full nandroid backup to be able to restore the Ubuntu bootimage directly from the CWM later)
- Simply restore the Android bootimage from the nandroid backup made before the installation of Ubuntu

HOW-TO:
To do that:
- Reboot on CWM (see the sticky, at the end)
- Go to 'backup and restore', then 'advanced restore'
- Choose the Android backup made before installing Ubuntu
- Choose 'Restore boot' option
- Wait until the restore is done...
- Choose 'reboot system now' to boot in Android

--------

- DUALBOOT Android/Ubuntu -

Introduction:
We can note that the both systems are installed on two different storage devices.
Android is directly on the device and Ubuntu is on the MicroSD.
The only thing that changes between the two systems is the bootimage.
If you have a nandroid backup of each WORKING systems, you can do an advanced restore of the boot 'boot.img'
of Ubuntu to boot it from the MicroSD card, or restore the boot of the Android backup to boot on Android !

HOW-TO:
To do that:
- Reboot on CWM (see the sticky, at the end)
- Go to 'backup and restore', then 'advanced restore'
- Choose the correct backup (the Android one, or the Ubuntu one)
- Choose 'Restore boot' option
- Wait until the restore is done...

--------

STICKY:
- Booting the Prime on recovery mode (CWM):
1. Power off the device (using Android, or by a long press of the power switch)
2. Power it on, by keeping simultaneously pressed the power switch and the volume down button
3. When text displays on top of the screen, release all, and press the volume up button
4. Wait a few seconds and CWM will appear on the Prime...

- Booting the prime in fastboot mode:
1. Power off the device (using Android, or by a long press of the power switch)
2. Power it on, by keeping simultaneously pressed the power switch and the volume down button
3. Wait until the message saying 'OS will coldboot in 10 seconds' etc... then release all buttons
4. Use the volume down button to select the USB icon
5. Validate with volume up
6. You can connect your device to a computer to send fastboot commands...

This is really great news!!!...I wanted to run ubuntu on my prime and use it as fully fledged portable laptop...
all there already was had either ubuntu running through vnc server and that too outdated version or chroot ubuntu...(if i am not missing anything here)

I wish that we would be soon able to get ubuntu for android (UFA) from canonical preinstalled with the next update of tf201...I heard that we cannot possibly install it without asus agreeing to team up with canonical...

As I said at the beginning, this is the work of lilstevie. I searched how to install it, and once I've set it up on my Prime, I made that tutorial today.
I share it here if someone want to try installing Ubuntu on their Prime.

The files are the original ones hosted by lilstevie. And I did not found any version newer, so let's wait for a new release, or a final version.

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